Mathematical Sciences: Foundations and Applications of Bayesian Inference and Decision Theory

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This project addresses Bayesian nonparametric procedures which incorporate information about the mean and about the tail behavior of the sampling distribution. Extensions to non-random samples from finite populations may be developed, drawing on a Bayesian theory of randomization. Extensions for censored data in the presence of covariates should also follow. Foundational issues for Bayesian theory of statistical inference revolve around assembling past information or prior opinion with new information or data and then presenting the amalgamated view. The inclusion of subjective views with information from observations has important implications for the applications of Bayesian inference and for effective statistically-based prediction and decisions. This research examines both fundamental mathematical issues and their applications to specific scientific questions.